A circular loop of wire with radius 2.00 cm and resistance 0.600 Ωis in a region of a spatially

step 1 Hi, in the given experiment, radius of the wire used is R is equal to 0 .80 millimeter or we can

A circular loop of wire with radius 2.00 cm and resistance...

A circular loop of wire with radius $2.00 \mathrm{~cm}$ and resistance $0.600 \Omega$ is in a region of a spatially uniform magnetic field $\vec{B}$ that is perpendicular to the plane of the loop. At $t=0$ the magnetic field has magnitude $B_{0}=3.00 \mathrm{~T}$. The magnetic field then decreases according to the equation $B(t)=B_{0} e^{-t / \tau},$ where $\tau=0.500 \mathrm{~s}$. (a) What is the maximum magnitude of the current $I$ induced in the loop? (b) What is the induced current $I$ when $t=1.50 \mathrm{~s} ?$

Key Concepts

Lenz's Law

Lenz's Law provides the direction of the induced current in response to a change in magnetic flux. It states that the induced current will flow in such a way as to oppose the change that produced it, ensuring the conservation of energy within the electromagnetic system.

Ohm's Law

Ohm's Law relates the current flowing through a conductor to the voltage across it and the resistance of the conductor. When an emf is induced in an electrical circuit, the resultant current can be determined by dividing the emf by the resistance, linking electromagnetic induction to measurable current.

Exponential Decay in Magnetic Fields

Exponential decay describes a process where the magnetic field decreases at a rate proportional to its current value. This mathematical behavior is common in physical systems experiencing a reduction in energy, and when applied to magnetic fields, it allows for determination of the time-dependent behavior of the induced current.

Faraday's Law of Induction

This law states that a changing magnetic flux through a closed loop induces an electromotive force (emf) in the loop. It is central to understanding how electric currents are generated by time-varying magnetic fields, and it forms the basis for devices such as generators and transformers.

Magnetic Flux

Magnetic flux is a measure of the amount of magnetic field passing through a given area. In the context of a loop, it is calculated as the product of the magnetic field strength and the area of the loop perpendicular to the field. Changes in this flux, either due to variations in the field strength or the area, lead to the induction of an emf.

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